Reviews in Computational Chemistry Volume 18

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122 Polarizability in Computer Simulations (monomer and dimer geometry, dipole moment, and/or polarizability; second virial coefficient) and the bulk liquid (thermodynamic, structural, and dynamic properties). 30,36,52,53,126,166,185 The expectation is typically that such models will also be able to perform well at conditions intermediate between gas and liquid phases, such as clusters and interfaces. It is also assumed that a reasonably correct treatment of polarization will allow for some extrapolation beyond these conditions, so that systems where the electric field is not as homogeneous as in bulk water can be treated. Even so, there are properties of small clusters and the bulk liquid that remain fairly elusive. For example, many models, both polarizable and nonpolarizable, do a poor job of reproducing the geometry of the water dimer. The methods typically predict a dimer that is too ‘‘flat’’, that is, with too small an angle between the donated O H bond on the donor and the C2v axis of the acceptor. This lack of tetrahedral coordination at the oxygen acceptor is usually attributed to the lack of lone pairs in the model; the electrostatic potential is insufficiently anisotropic on the oxygen end of the molecule when only atom-centered charges and dipoles are used. Models with off-atom charge sites, 54,166 higher order multipoles, 21,193 or explicitly anisotropic potentials 15,193 can be used to avoid this problem. For gas-phase properties, the second virial coefficient, B(T), provides one of the most sensitive tests of a water model. 186,194 Both polarizable and nonpolarizable models are capable of reproducing experimental values of B(T), and some models have even been parameterized to do so explicitly. 15,24,29 Polarizable models appear to provide significant improvements in reproducing not only the second virial coefficient, 24,25 but also the third coefficient, C(T). 186,195 In the liquid phase, calculations of the pair correlation functions, dielectric constant, and diffusion constant have generated the most attention. There exist nonpolarizable and polarizable models that can reproduce each quantity individually; it is considerably more difficult to reproduce all quantities (together with the pressure and energy) simultaneously. In general, polarizable models have no distinct advantage in reproducing the structural and energetic properties of liquid water, but they allow for better treatment of dynamic properties. It is now well understood that the static dielectric constant of liquid water is highly correlated with the mean dipole moment in the liquid, and that a dipole moment near 2.6 D is necessary to reproduce water’s dielectric constant of e ¼ 78. 4,5,185,196 This holds for both polarizable and nonpolarizable models. Polarizable models, however, do a better job of modeling the frequency-dependent dielectric constant than do nonpolarizable models. 126 Certain features of the dielectric spectrum are inaccessible to nonpolarizable models, including a peak that depends on translation-induced polarization response, and an optical dielectric constant that differs from unity. The dipole moment of 2.6 D should be considered as an optimal value for typical (i.e.,
Applications 123 classical and rigid) water models; it is not necessarily the best estimate of the actual dipole moment. The dipole moment of liquid water cannot be measured experimentally, nor can it even be defined unambiguously, since the electronic density is not zero between molecules. 197,198 Ab initio simulations of liquid water predict that the average dipole moment varies from 2.4 to 3.0 D depending on how the density is partitioned, so a value of 2.6 D is consistent with these studies. 199–201 Dynamic properties, such as the self-diffusion constant, are likewise strongly correlated with the dipole moment. 5,23 This coupling between the translational motion and the dipole moment is indicated in the dielectric spectrum. 126 Models that are overpolarized tend to undergo dynamics that are significantly slower than the real physical system. The inclusion of polarization can substantially affect the dynamics of a model, although the direction of the effect can vary. When a nonpolarizable model is reparameterized to include polarizability, the new model often exhibits faster dynamics, as with polarizable versions of TIP4P, 202 Reimers–Watts–Klein (RWK), 185,203 and reduced effective representation (RER) 30 potentials. There are exceptions, however, such as the polarizable simple point charge (PSPC) 23,57 and fluctuating charge (FQ) 126 models. The usual explanation for faster dynamics in polarizable models is that given by Sprik. 202 Events governing dynamical properties, such as translational diffusion and orientational relaxation, are activated processes—they depend on relatively infrequent barrier-crossing events. Adiabatic dynamics of the polarizable degrees of freedom allows for relaxation of the polarization at the transition, through means that are inaccessible to nonpolarizable models. This in turn lowers the activation barrier and increases the number of successful transition attempts. The nonunanimity of published simulation results concerning dynamic properties is likely due to such factors as: inconsistent parameterization procedures between the polarizable and nonpolarizable models; a strong dependence of dynamic properties on the system pressure (which is often insufficiently controlled during simulations); and the effects of using point versus diffuse charge distributions. Transferability to different temperatures is a particularly difficult task for polarizable water models. This statement is illustrated by the problems in predicting the PVT and phase coexistence properties. There are a handful of polarizable water models—including both dipole- and EE-based models— that are reasonably successful in predicting some of the structural and energetic changes in liquid water over a range of several hundred degrees. 53,61,204 Many models fail to capture this behavior, however, so temperature transferability is far from an automatic feature of polarizable models. 35,52,61,62 Indeed, it has been demonstrated by several authors 35,52,61 that a point dipole-based model designed specifically to reproduce properties of the gas-phase monomer and the bulk liquid at 298 K is doomed to fail at higher temperatures. This failure could arise from insufficiencies in the Lennard–Jones function typically
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Reviews in Computational Chemistry
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Kenny B. Lipkowitz Department of Ch
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vi Preface three-dimensional struct
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viii Preface some descriptors and i
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Epilogue and Dedication My associat
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Contents 1. Clustering Methods and
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Contents xv Electron Transfer in Po
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Contributors John M. Barnard, Barna
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Contributors to Previous Volumes *
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Volume 3 (1992) Tamar Schlick, Opti
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Volume 7 (1996) Geoffrey M. Downs a
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Volume 11 (1997) Mark A. Murcko, Re
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T. Daniel Crawford* and Henry F. Sc
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Topics Covered in Volumes 1-18 * Ab
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Reviews in Computational Chemistry
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2 Clustering Methods and Their Uses
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10 Clustering Methods and Their Use
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42 The Use of Scoring Functions in
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Table 1 Reference List for the Most
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Page 117 and 118: CHAPTER 3 Potentials and Algorithms
Page 119 and 120: Vn (1 + cos(nω + γ)) 2 K θ (θ
Page 121 and 122: are modified by their environment w
Page 123 and 124: Table 1 Polarizability Parameters f
Page 125 and 126: The polarizable point dipole models
Page 127 and 128: two to three orders of magnitude sl
Page 129 and 130: M i z i + q i d i k i and shell cha
Page 131 and 132: Shell Models 103 on estimates of sh
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Page 135 and 136: The energy required to create a cha
Page 137 and 138: for all i ði:e:; 8 iÞ: @U @qi l
Page 139 and 140: where we have used q Cl ¼ qNa. The
Page 141 and 142: Electronegativity Equalization Mode
Page 143 and 144: Electronegativity Equalization Mode
Page 145 and 146: of N molecules is taken as a Hartre
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Page 149: water have been developed, includin
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Page 155 and 156: Comparison of the Polarization Mode
Page 157 and 158: negligible errors in such propertie
Page 159 and 160: ecome significant at field strength
Page 161 and 162: noteworthy in this regard because t
Page 163 and 164: References 135 9. P. Cieplak and P.
Page 165 and 166: References 137 48. E. L. Pollock an
Page 167 and 168: References 139 Computational Chemis
Page 169 and 170: References 141 139. J. Hinze and H.
Page 171 and 172: References 143 178. J. J. P. Stewar
Page 173 and 174: References 145 216. M. W. Mahoney a
Page 175 and 176: CHAPTER 4 New Developments in the T
Page 177 and 178: Introduction 149 applications). For
Page 179 and 180: FCWD(∆E ) FCWD(0) ∆E = 0 ∆E
Page 181 and 182: Introduction 153 Equations [6]-[12]
Page 183 and 184: Paradigm of Free Energy Surfaces 15
Page 185 and 186: Paradigm of Free Energy Surfaces 15
Page 187 and 188: In Eqs. [18] and [19], F0i is the e
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βF i (X ) 40 20 0 −20 1 2 βλ 1
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Table 1 Main Features of the Two-Pa
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and Hss ¼ U rep ss 1 2 X j;k ðmj
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λ i /eV 4 3 2 1 0 0 10 20 30 40 Bo
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the width/Stokes shift relation (Eq
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Table 3 Mapping of the Q Model on S
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This situation is of course not sat
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F ± (Y ad )/λ I 0.8 0.4 0 −0.4
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it by choosing the GMH basis set 7
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Anharmonic higher order terms gain
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of the radiation is the perturbatio
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individual vibrational excitations
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m 12 /D 6 5.5 5 4.5 4 3.5 17 18 19
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In Eq. [144], the coordinates Y km
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ε/M −1 cm −1 4000 2000 0 analy
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βσ 2 /10 3 cm −1 14 12 10 8 Opt
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0.2 0.1 0 12 16 20 24 28 32 The app
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References 207 7. M. D. Newton, Adv
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References 209 59. R. Kubo and Y. T
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